Quasi-null lens optical system for the fabrication of anoblate convex ellipsoidal mirror: application to the WideAngle Camera of the Rosetta space mission
Maria-Guglielmina Pelizzo, Vania Da Deppo, Giampiero Naletto, Roberto Ragazzoni,and Andrea Novi
The Rosetta is the European Space Agency corner-stone mission dedicated to close observations of the67P�Churyumov–Gerasimenko comet.1 The Rosettawas launched in March 2004, and it will approachthe comet in 2014. The probe will then orbit in thecomet’s gravity field and will make observations of itsnucleus and coma; in addition, a Surface SciencePackage module will land on the comet’s surface tomake in situ observations.
The Wide Angle Camera2,3 (WAC) and the Nar-row Angle Camera4 (NAC) are the two cameras ofOSIRIS, the scientific imaging system of the probe.5,6
During the first fly-bys the two cameras will acquireimages of Mars and Earth; during the probe naviga-tion they will collect images of asteroids; during therendezvous with the comet they will be used to guide
the Surface Science Package module’s landing on thecomet surface, and they will acquire images of thecomet’s surface, coma dust, and gas jets at differentwavelengths. From a technical point of view, one ofthe most interesting aspects of the WAC is its opticaldesign, based on an innovative off-axis two-mirrorconfiguration.3,7 In this design, the primary mirror(M1) has a convex oblate ellipsoidal surface withquite a large conic constant. One of the most chal-lenging tasks in the camera’s realization was the fab-rication and characterization of this mirror.
The fabrication of an aspheric mirror is usuallyperformed by a preliminary rough mirror shaping bymeans of a numerically controlled machine, followedby a fine polishing monitored by an interferometricsetup: By minimizing the difference between the ac-tual and the nominal interferogram, the correct shap-ing of the surface is finally obtained.8 Interferometrictesting of aspheric surfaces often requires a compen-sator (a null lens) element that suitably shapes thespherical or plane wave exiting the interferometer tocompensate for the deformation introduced by thespecific surface under test. This compensator, usuallymore complex than a single lens, is rather criticalsince it requires both an optimal manufacturing andhigh precision relative positioning with respect to thesurface to be polished.9 By means of this suitable tool,the optimal surface is reached when a null interfero-gram is obtained.
To maintain a simple and low cost, but at the sametime realize a very reliable interferometric test forthe fabrication of the WAC M1 mirror, we have de-
M.-G. Pelizzo ([email protected]), V. Da Deppo, and G. Nal-etto are with CNR-INFM-LUXOR-Laboratory for Ultraviolet andX-ray Optical Research, Via Gradenigo, 6�B-35131, Padova, PD,Italy and with the Dipartimento di Ingegneria dell’Informazione,Via Gradenigo, 6�B-35131, Padova, PD, Italy. G. Naletto is alsowith CISAS-Centro Interdipartimentale Studi e Attività SpazialiG. Columbo, Via Venezia, 15-35131 Padova, PD, Italy. R. Ragaz-zoni is with INAF Osservatorio Astrofisico di Arcetri, Largo E.Fermi 5, 50125 Firenze, FI, Italy. A. Novi is with Galileo Avionica,Via A. Einstein 35, 50013 Campi Bisenzio, FI, Italy.
Received 3 January 2006; accepted 3 March 2006; posted 27March 2006 (Doc. ID 67036).
signed a quasi-null lens system based on a singlerefractive optic with spherical surfaces used as com-pensators. This system, realized by Galileo Avionica(Campi Bisenzio, Italy), has made possible a verysuccessful test of this particular mirror.
2. Wide Angle Camera Optical Design
The WAC of the Rosetta mission adopts an innovativeoff-axis two-mirror optical configuration.7 It performsat a diffraction limit over a rather large 12° � 12°field of view (FOV). The optical schematic of the cam-era is sketched in Fig. 1, and its characteristics aredescribed in Ref. 3. The camera design is based on anoff-axis portion of a convex oblate ellipsoidal primarymirror, M1, and a concave oblate secondary one, M2.The parameters for the two mirrors are reported inTable 1. The formula used for defining the conic sur-face is
x�y, z� �1
c�k � 1� �1 � �1 � (k � 1)c2r2�, (1)
where r2 � y2 � z2, k is conic constant parameter, andR � 1�c is the radius of curvature at the surfacevertex. The tolerance analysis performed on thewhole WAC design has set M1 shape tolerance valuesequal to �0.1 mm on the vertex radius and �0.03 onthe conic constant (see Table 1).
The M1 has been realized by cutting two off-axismirror portions from an assosymmetric parent mirrorof 150 mm diameter; therefore the whole parent mir-ror had to be polished to optical quality. This mirrorwas extremely difficult to realize; in fact, the differ-ence at the edges of the substrate between the mirrorsurface and its best-fit sphere is of the order of380 �m. This implies the removal of a large amountof glass material and a relatively large local slope. Asa consequence, during the fine polishing activity the
control of the mirror’s optical quality on the glasssubstrate has to be extremely accurate.
3. Quasi-Null Lens System Design
To achieve an interferometric setup to monitor theoptical quality of the 150 mm diameter assosymmet-ric ellipsoidal parent mirror during the fine-polishingphase, different optical schemes had to be taken intoconsideration. All the configurations were designed toobtain a null lens system.
In the first scheme [see Fig. 2(a)] a positive lensfocuses the laser beam toward the ellipsoidal surface.With this configuration the mirror is tested frontally,and the laser beam is reflected by the mirror surface.Even if rather simple in theory, this classical solutionhad to be discarded. In fact, simulations performedwith a ray-tracing code have shown that the theoret-ical compensator is a very large aspherical lens, crit-ical to be realized. This fact, together with the highoptical quality requirements for this lens, meant thatthe null lens would have been more difficult and ex-pensive to realize than the mirror itself. Moreover, inthis configuration the laser beam diameter shouldhave been larger than what was available from theinterferometer.
In the second scheme [Fig. 2(b)], the sample beamis refracted by the null lens, passes through the mir-ror substrate and is backreflected by the mirror’sblank flat surface. In this way, the laser beam sizeand the null lens are smaller than those necessary inthe first scheme. Obviously, to perform this test therear flat surface of the mirror blank had to be pol-ished to interferometric quality. The results of thesimulations showed that the optimal null lens is ameniscus lens with aspherical surfaces; unfortu-nately, as in the first scheme, this kind of optic re-quires a great deal of effort to produce.
Fig. 1. Optical scheme of the WAC.
Table 1. M1 and M2 Mirror Characteristics
Radius orCurvature
(mm)Conic
Constant Shape Size
M1 406.6 � 0.1 5.71 � 0.03 Square 50 mm � 50 mmM2 400.0 � 0.1 0.16 � 0.03 Circular D � 61 mm
Finally, a third solution has been considered, asshown in Fig. 2(c). This scheme is similar in principleto the second scheme, but in this case the mirror isreversed: The laser beam impinges the flat surface,passes through the blank substrate and is backre-flected by the surface under test at its concave side.The results from the simulations show that in thisdesign the nominal compensating element is a bicon-cave lens, also, in this case, with aspherical surfaces.The need to realize aspherical optical surfaces to ob-tain a null system still remains, but in this last case,in contrast to the others, the lens surfaces do notdiffer too much from the spherical ones. This factmade us consider the possibility of adopting a quasi-null lens system that is an optical system in whichsome residual aberrations were still present, butwhose relative amount of fringes in the interferogramwere rather low. In fact, the knowledge of the fringepattern from ray tracing allows us to use this methodto control the mirror polishing by subtracting in realtime this pattern from the interferogram acquired toobtain a null lens synthetic pattern.
In this perspective, the scheme shown in Fig. 2(c)can be realized adopting a biconcave lens with simplespherical surfaces. Since the illuminating beam andthe null lens size are also small, this solution hasbeen adopted for testing the mirror surface opticalquality. Obviously, the system allows good control ofthe mirror surface only if the flat rear mirror surfaceis also polished to interferometric quality level. Asketch of the design of the quasi-null lens systemderived by the optimization of the optical scheme justdescribed is shown in Fig. 3. The null lens opticalcharacteristics are summarized in Table 2.
From the simulations performed to evaluate thecapability of the system, the interferogram shown in
Fig. 4 has been obtained. The presence of somefringes in the nominal configuration is actually due tothe imperfect compensation of the system (i.e., this isa quasi-null lens system). Nevertheless, the systemcan be efficiently applied to perform the polishing ofthe mirror once this nominal interferogram is sub-tracted in real time from the interferometric imagesacquired. Figure 5 shows the wavefront profile plot ofthe interferogram itself along a pupil diameter (thesystem is rotationally symmetric); that residualamount of uncompensated wavefront has a peak-to-valley (PTV) value of only 0.44� at 632.8 nm. Theresidual aberration Zernike coefficients, obtained bythe interferometric analysis (p is the normalized ra-dial coordinate on the exit pupil of the null lens op-tical system) are reported in Table 3. As shown, theaberration coefficients are quite small.
Since the ellipsoidal mirror is tested from the backand the radiation is backreflected from the glass side,this system is 1.5 times more sensitive to �x errors
Fig. 3. Project of the quasi-null lens.
Fig. 4. Theoretical interferogram obtained by simulation.
Fig. 5. Optical path difference (measured in wavelengths, where� � 632.8 nm) with respect to chief ray as a function as thenormalized radial coordinate p on the exit pupil of the opticalsystem.
Table 2. Bi-Concave Quasi-Null Lens Parameters
R1 (radius of curvature first surface) �121.54 mmR2 (radius of curvature second surface) 280.18 mmThickness (at center) 10 mmDiameter 90 mmMaterial BK7Distance M1-lens vertex 92.62 mm
(for the x axis direction see Fig. 2) then the usualsetups in which the illumination of the surface undertest comes from the front side, a fact that character-izes this system as a very powerful tool. In fact, let usconsider two points, A and B, on a plane wavefrontimpinging on a BK7 substrate (i.e., our mirror) (seeFig. 6); if a defect of �x height is present on the backside of the substrate (i.e., the primary surface mir-ror), the traveling times inside the glass for opticalpaths A and B are not equal, but they are, respec-tively, tA � 2L�v and tB � 2�L � �x��v, where L is thethickness of the substrate and v is the speed of lightin BK7. The optical path difference, as seen by theinterferogram, is then
s � �tA � tB�c � 2�xvc � 2n�x � 3�x. (2)
Therefore the so-called physical wedge factor to beconsidered in this interferometric analysis is 1�3 �0.33, to be compared with the 1�2 � 0.5 factor usedfor the front-side setups.
To have a reasonable certainty about the results ofthe described procedure, a sensitivity analysis of theinterferometric setup was also performed by simulat-ing the whole system by using the given mirror tol-erances reported in Table 1. This analysis has shownthat a change in the M1 radius of �0.1 mm is essen-tially equivalent to introducing a spherical aberra-tion in the quasi-null lens system, which can becompensated for by varying the nominal distance be-tween the mirror and the biconcave lens of �60 �m.This means that the system is indeed rather insen-
sitive to realistic variations of the radius of the parentmirror with respect to the nominal one, and thereforethat the radius of the optics has to be measuredindependently. Conversely, a variation of the conicconstant value of �0.03 is only very partially com-pensated for by varying the nominal distance be-tween the mirror and the biconcave lens of �50 �m.This demonstrates that this system is very sensitiveto possible variations of the conic constant with re-spect to the nominal value.
Tolerances related to the alignment of the inter-ferometric setup have also been investigated. First, itis necessary to observe that all the optical compo-nents of the interferometric system have been real-ized by means of rotationally symmetric machines.This has the consequence that significant nonaxialsymmetric aberrations can be present in the systemonly if there are some misalignments of the optics,such as tilt and�or decentering. Actually, it is possi-ble that the flat back surface of the mirror is notexactly coaxial with the conic front surface, and alsoin this case some nonaxial symmetric aberrations ascoma would be present in principle. However, owingto the requirement of 1 arc min tolerance for thecoaxiality between the two mirror surfaces given tothe optics producer, the simulations performed haveproven that this effect is negligible. Under these hy-potheses, it is clear that if some nonaxial aberrationsare present in the interferogram when the mirror isunder test, the optical elements of the system are notwell aligned (for example, it has been verified that atilt of the lens of 0.01° with respect to the z axis gives
Fig. 6. Optical path difference in the reflected wavefront whenilluminating a mirror from the back side.
Fig. 7. Interferogram acquired during the polishing phase of oneof the mirrors.
Table 3. Theoretical Values of the Residual Aberrations Expressed inTerms of Zernike Coefficients
a Zernike aberration coefficient of Z8 � 0.7 �). Thismeans that the interferometer itself can be used tovalidate the alignment of the setup: The system isoptimally aligned when all the nonaxial aberrationsare minimized on the interferogram. Owing to theextreme accuracy of the interferometer, this tech-nique allows us to obtain an extremely accuratealignment of the system. Finally, regarding possiblemisalignments due to nonprecise axial positioning ofthe optics, we can observe that these translate intodefocus and spherical aberrations on the interfero-gram that are not of interest for this measurement.Since the light must travel inside the mirror sub-strate, another important factor that could affect theinterferogram is the material homogeneity. In thiscase, a very standard material such as BK7 has beenadopted to realize the mirror substrate, and the glassproperties have been guaranteed by Schott certifica-tion.
4. Quasi-Null Lens Fabrication
The quasi-null biconcave lens has been fabricatedand tested by Galileo Avionica, Campi Bisenzio,Italy. The radius of curvature of the two lens sur-
faces has been measured with a profilometer; thevalue of the radius of curvature of the first lenssurface is R1 � 121.58 mm, against the theoreticalvalue of 121.54 mm, and the radius of curvature ofthe second lens surface is R2 � 280.20 mm (theoret-ical value 280.18 mm). These very small variationswith respect to the nominal radii do not affect thesystems performance, but they require a minor ad-justment of the nominal distance between the lensand the mirror to be tested, bringing it to 92.58 mm.In Table 4 the third-order Seidel aberration coeffi-cients related to each one of the spherical surfaces ofthe biconcave lens obtained by an interferometricanalysis are reported. Since the PTV value is 0.198 �at 632.8 nm, and the rms value on the surfaces isbetter then ��20, the error introduced in the inter-ferometric setup by the quasi-null lens can be as-sumed negligible.
5. Mirror Realization
A total of six M1 mirrors were requested from GalileoAvionica: the two of lowest quality for the WACbreadboard, the two of best quality for the WAC qual-ification and the flight models, and the remaining twoas spares. To realize all these mirrors, three parentmirrors were shaped by a numerically controlled ma-chine (Carl Zeiss Incorporated).
Before beginning the polishing activity, a series ofmetrological measurements were performed on themirrors under test, including a measurement of theradius by means of a profilometer, scanning the sur-face along three different diameters. By fitting theacquired profile with a surface having the nominalconic constant (i.e., 5.71), the radius of the mirrorswas established. As already mentioned, a variation ofthe radius of the parent mirror with respect to thenominal one requires a small adjustment of the dis-
Fig. 8. Interferogram acquiredat the end of the polishing phaseof one of the mirrors once the syn-thetic one is subtracted.
Table 5. Zernike Coefficients of One of the M1 Mirrors after Polishingin the Quasi-Null Lens Setup
tance between the mirror itself and the biconcavelens to compensate for the spherical aberration.
At this point the mirrors were polished by using thequasi-null lens setup to monitor their shape. In Fig. 7the acquired interferogram obtained in one of thepolishing sessions is shown to be compared with thenominal one of Fig. 4. In Table 5, the Zernike coeffi-cients corresponding to the postpolishing interfero-gram of Fig. 8 obtained by removing the syntheticinterferogram, are reported: they show a very lowamount of aberration residuals, with a PTV of 0.88 �and an rms value of 0.146 �. All six mirrors werefabricated by Galileo Avionica within specification(the flight M1 mirror is shown in Fig. 9), a fact thatconfirms the capabilities of the control method imple-mented with this simple quasi-null lens system.
For a final and complete verification of the qualityof the whole integrated WAC instrument, an inter-ferometric test was performed using a Zygo inter-ferometer (Fig. 10): the collimated beam exiting theinterferometer is focused on the focal plane of thecamera, once the detector is removed. The beam isthen nominally collimated by the two mirrors, and isbackreflected inside the camera by a plane mirrorplaced in a suitable position. It then returns to theinterferometer where the interferogram is produced.The residual aberrations measured by the interfero-gram with this setup are compared with the theoret-ical ones for the central point of the FOV in Table 6.Thanks to the high quality of the fabricated mirrorand to the proper alignment, the optical perfor-mances of the WAC have been demonstrated to be
extremely good. An extensive presentation of themeasured camera performances is reported in Ref.10. Actually, not only the end-to-end tests performedon the ground, but also the first images acquiredwith the WAC in flight, show that the optical per-formances of this instrument is excellent, with aninstrument point-spread function at the limit of dif-fraction.
6. Conclusions
A very innovative, simple, low-cost and reliablequasi-null lens setup has been designed to fabricate aconvex oblate ellipsoidal mirror characterized by arelatively high value of the conic constant. The the-oretical performances and technological aspects re-lated to the realization of the system have been theobject of this study. An experimental setup has beenrealized to fabricate the primary mirror of the WACof the OSIRIS instrument onboard the Rosetta ESAmission. This mirror has been successfully realizedand tested, and the performance goal of the WACinstrument has been achieved.
The authors acknowledge the assistance of all theOSIRIS team, as this work is just a part of the hugeeffort in the realization of the whole Rosetta imagingsystem. This work has been supported by a grantfrom the Italian Space Agency for the realization ofthe WAC.
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